I think that's the igniter wire. The outer covering is thick, waxy plastic, not the normal pvc. It leads to the spark electrode at the burner end, and to the thing that generates the high voltage at the detached end. My first guess would be into an orifice on that orange thing in the picture, but on looking more closely, I think it may go to the terminal at the very bottom left, which is labelled "HT" It presumably should have a female spade connector on the end, but at that voltage, just about anything secure will do